The extension problem for partial Boolean structures in Quantum Mechanics

TL;DR

This paper explores the extension problem for partial Boolean structures in quantum mechanics, providing an algebraic framework that generalizes existing techniques and discusses implications for classical representability and Bell inequalities.

Contribution

It introduces an algebraic approach to partial Boolean structures, enabling reduction of contexts and generalizing methods for classical extension in quantum mechanics.

Findings

Characterization of partial Boolean structures in quantum predictions

Generalization of classical extension techniques

Implications for Bell inequalities and classical representability

Abstract

Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the number of contexts, classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.